The length of rod in terms v(r) and t is L = [ Δt / (1/343) - (1/v(r)) ].
3.56 km/s is the speed of a one-dimensional compressional wave moving along a thin copper rod.
At one end of the rod, a hard hammer strike is delivered. With a time interval of Δt between the two pulses, a listener at the other end of the rod hears the sound twice as it travels through the metal and the air.
The time interval is given by t = L/v.
The delay between pulses arrivals is:
Δt = L [(1/v(air)) - (1/v(copper))]
Now,
When the copper rod is swapped out for a different substance and the sound speed is measured as v(r).
The speed of air, v(air) = 343 m/s
Then,
L = [ Δt / (1/v(air)) - (1/v(r)) ]
L = [ Δt / (1/343) - (1/v(r)) ]
Here L is the length of the rod, Δt is in seconds and v(r) is the speed of sound in the rod.
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